Discontinuous Galerkin finite element modelling of geophysical and environmental flows.
Numerical models are essential tools in modern oceanography and limnology. They are used in various domains, from climate change studies to forecasting of storm surge or contaminant transport. Over the last decade, unstructured mesh models have proved their efficiency in simulating multiscale hydrodynamics in complex topographies. However, numerous challenges and limitations still need to be addressed. Philippe Delandmeter's thesis focuses on the development of the unstructured mesh Second-generation Louvain-la-Neuve Ice-ocean Model (SLIM, www.climate.be/slim), based on the discontinuous Galerkin finite element method, and especially its three-dimensional version, SLIM 3D. Two key aspects of the model development are tackled: model validation and the improvement of SLIM 3D accuracy and stability.
High-resolution models such as SLIM can resolve flow features with a size of a hundred metres but how accurate are those results? Using new stereo high-resolution satellite imagery, which is used to measure the water velocity with an unprecedented resolution, SLIM modelling of tidal eddies in the wake of coral islands in the Great Barrier Reef, Australia, is validated.
To study complex hydrodynamics, SLIM 3D stability is increased by modifying the pressure gradient computation and by handling a discrete bathymetry. Moreover, its accuracy is greatly improved with a new vertically adaptive mesh as well as a conservative and consistent formulation of the tracer equation. The improved model is used to simulate thermocline oscillations in Lake Tanganyika, East African Rift, and the transport of the sediment exported by the Burdekin River, Australia.